curve #6250

y² + xy = x³ + x² − 264347120208447x + 1449524328508096697385

a-invariants: [1, 1, 0, -264347120208447, 1449524328508096697385]
c-invariants: [12688661770005481, -1252389114995958821581685]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 152021288284679676420402639931235696997162
discriminant (Δ): 274550446642131495615247167715811668776874572
Faltings height: 7.2544
naive height: 111.2385
primes of bad reduction: 2, 3, 7, 43, 84175685650431714518495370947528071427
regulator: 35959548414759.81327587371165044439191555781361220700150670271185051917
submitted by: The Wren
submitted at: 2026-10-31 22:51:22 UTC
last updated: 2026-10-31 22:51:22 UTC

Witness: 16 independent points log in to add more points →

(-11498008, -54481910019)
(12661087364, -1424649664640961)
(-243804642/169, -93928254126933/2197)
(94734103022/4489, -21836162944709475/300763)
(152738137/9, -1161898286495/27)
(5239863896/361, -177666113943879/6859)
(10065510398/841, 8090975755115/24389)
(1450399355/121, 2353402773255/1331)
(14158752958/1089, 521042042548967/35937)
(-17280562, 29288457507)
(-53008437/4, 409959709821/8)
(316932, 36956249661)
(12909921, 13721974275)
(26427614, 113657378347)
(33561359, 174281845689)
(420860814/25, 5258221573227/125)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 16 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_16.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 22:51:22 UTC · history